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A bound on the spectral radius of graphs with \(e\) edges. (English) Zbl 0617.05045

Author’s abstract: ”The spectral radius \(\rho(A)\) of the adjacency matrix \(A\) of a graph \(G\) with \(e\) edges satisfies \(\rho(A)\leq (- 1+\sqrt{1+8e})/2\). Equality occurs if and only if \(e=\binom{k}{2}\) and \(G\) is a disjoint union of the complete graph \(K_k\) and isolated vertices.”

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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References:

[1] Brualdi, R. A.; Hoffman, A. J., On the spectral radius of (0,1)-matrices, Linear Algebra Appl., 65, 133-146 (1985) · Zbl 0563.15012
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